What is 3/21 plus 2/3? (Answer: 17/21)

Exact Answer

==================================================
Problem: What is 3/21 plus 2/3?
Formula / Expression: 3/21 + 2/3
Final Answer: 17/21
==================================================

Step-by-Step Solution:

Step 1: Find the Least Common Denominator (LCD)
Notice that 21 is an exact multiple of 3 (3 × 7 = 21). The Least Common Denominator (LCD) is simply 21, meaning we only need to scale one fraction.
Working: LCD(21, 3) = 21

Step 2: Convert to Equivalent Fractions with Common Denominator 21
Multiply the numerator and denominator of 3/21 by 1, and multiply the numerator and denominator of 2/3 by 7 so both fractions share the common base 21.
Working: 3 × 1/21 × 1 = 3/21 and 2 × 7/3 × 7 = 14/21

Step 3: Add the Numerators
Now add the numerators (3 + 14 = 17) and keep the common denominator 21 unchanged.
Working: 3 + 14/21 = 17/21

Step 4: Check if the Fraction Can Be Simplified
The Greatest Common Divisor (GCD) of 17 and 21 is 1, confirming that 17/21 cannot be reduced further—it is already in its simplest irreducible form.
Working: 17/21

Step 5: Decimal & Percentage Representation
Dividing the numerator 17 by denominator 21 produces a repeating decimal (approximately 0.809524, or 80.9524%).
Working: 17 ÷ 21 = 0.809524 (80.9524%)

Key Values:
- Simplified Fraction: 17/21
- Mixed Number Form: 17/21
- Decimal Value: 0.809524
- Percentage: 80.9524%

--------------------------------------------------
Solved with FractionsCalc:
https://fractionscalc.com/what-is-3-21-plus-2-3/
==================================================

3/21 + 2/3 = 17/21

Simplified Fraction

17/21

Mixed Number

Proper (17/21)

Decimal Value

0.809524

Percentage

80.9524%

Reduce / Convert Fraction:

Convert Fraction:

Enter Decimal Number:

Enter Percentage: %

What is % of

From Value: To Value:

Simplify Ratio: :

Switch to Proportion / Missing X Solver (A/B = C/D) →

Enter 3 known numbers and leave 1 empty (or type x) to solve:

← Switch to Ratio Simplifier (A:B)

Provide any 2 values below to calculate the remaining:

Price before discount

Discount

Price after discount

You saved

+ Add Sales Tax & Extra Coupon (Optional)

Sales Tax: % Extra Off: %

Provide any 2 values below to calculate the remaining:

Cost

Markup

REVENUE

Gross Profit

Profit Margin

Bill Subtotal

Tip Percentage

Split (People)

👥

Quick Tip:

Total Bill

Split Between

👥

Tip % (Optional)

Include Tip:

Total Price

Quantity

Unit of Measure

← Discount & Sales Tax • Ratio Simplifier (A:B) →

First Number: Second Number:

Find All Factors of:

Dividend: ÷ Divisor:

Number to Round: To Nearest:

Method: Standard (5+ ↑) Always Up (Ceil) Always Down (Floor)

Presets:

√ Square Root of: OR Power (x^y): ^{^}

x² + x + = 0

Number (n! & log):

Circle Radius (r):

Side a: Side b:

Angle (Degrees): °

Numbers (comma separated):

Total Items (n): Choose (r):

Decimal Number:

Number (1–3999):

Step-by-Step Solution: 3/21 + 2/3

Step 1

Find the Least Common Denominator (LCD)

Notice that 21 is an exact multiple of 3 (3 × 7 = 21). The Least Common Denominator (LCD) is simply 21, meaning we only need to scale one fraction.

LCD(21, 3) = 21

Step 2

Convert to Equivalent Fractions with Common Denominator 21

Multiply the numerator and denominator of 3/21 by 1, and multiply the numerator and denominator of 2/3 by 7 so both fractions share the common base 21.

3 × 1/21 × 1 = 3/21 and 2 × 7/3 × 7 = 14/21

Step 3

Add the Numerators

Now add the numerators (3 + 14 = 17) and keep the common denominator 21 unchanged.

3 + 14/21 = 17/21

Step 4

Check if the Fraction Can Be Simplified

The Greatest Common Divisor (GCD) of 17 and 21 is 1, confirming that 17/21 cannot be reduced further—it is already in its simplest irreducible form.

17/21

Step 5

Decimal & Percentage Representation

Dividing the numerator 17 by denominator 21 produces a repeating decimal (approximately 0.809524, or 80.9524%).

17 ÷ 21 = 0.809524 (80.9524%)

Visual Representation

The diagram below illustrates 3/21 plus 2/3 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`17/21`
Mixed Number Form	`17/21`
Decimal Form	`0.809524`
Percentage	`80.9524%`

Was this solution helpful?

Help us improve our free step-by-step tools

Frequently Asked Questions

What is 3/21 plus 2/3 as a fraction?

3/21 + 2/3 in simplest fraction form is 17/21.

What is 3/21 plus 2/3 as a decimal?

3/21 + 2/3 converted to a decimal is 0.809524.

What is 3/21 plus 2/3 as a percentage?

3/21 + 2/3 expressed as a percentage is 80.9524%.

Does 3/21 plus 2/3 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.809524...) because the denominator contains prime factors other than 2 and 5.